Respuesta :
Answer:
The probability of getting 6's on both cubes is [tex]\frac{1}{36}[/tex].
The probability that the total score is at least 11 is [tex]\frac{1}{12}[/tex].
Step-by-step explanation:
Consider the provided information.
A red cube has faces labeled 1 through 6, and a blue cube has faces labeled in the same way.
Part (A) Both cubes show 6’s.
Probability of getting 6 on red cube is [tex]\frac{1}{6}[/tex]
Probability of getting 6 on blue cube is [tex]\frac{1}{6}[/tex]
Thus, the probability of getting 6's on both cubes is:
[tex]P(\text{Both 6's})=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}[/tex]
Hence, the probability of getting 6's on both cubes is [tex]\frac{1}{36}[/tex].
Part (B) The total score is at least 11.
The possible number of outcomes in which total score is at least 11 is:
Red shows 6 and Blue shows 5.
Blue shows 6 and Red shows 5.
Blue shows 6 and Red shows 6.
Thus, the probability of total score is at least 11.
[tex]P(\text{Total is at least 11})=\frac{1}{6}\times\frac{1}{6}+\frac{1}{6}\times\frac{1}{6}+\frac{1}{6}\times\frac{1}{6}\\P(\text{Total is at least 11})=\frac{1}{12}[/tex]
Hence, the probability that the total score is at least 11 is [tex]\frac{1}{12}[/tex].
